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Encyclopedia > Boolean value

In mathematics, a Boolean function is usually a function

F(b1, b2, ... , bn)

of a number n of Boolean variables bi from the two-element Boolean algebra {0,1}, and such that F also takes values in {0, 1}. A function on a general domain of a function taking values in {0, 1} would be called a Boolean-valued function, so that Boolean functions are a special case. Such a function with domain {1, 2, 3, ... } is commonly called a binary sequence, i.e. an infinite sequence of 0's and 1's; by restricting to { 1, 2, 3, ..., n } a Boolean function is in a natural way coded by a sequence of length n.


There are such functions; these play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers. The properties of boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see S-box).


See also

External links

  • Boolean Planet (http://www.isrc.qut.edu.au/people/fuller/) — boolean functions in cryptography.



  Results from FactBites:
 
Core JavaScript Reference: Boolean (600 words)
The Boolean object is an object wrapper for a boolean value.
For example, a Boolean object whose value is false is treated as the primitive value false, and a Boolean object whose value is true is treated as the primitive value true in conditional tests.
For Boolean objects and values, the built-in toString method returns the string "true" or "false" depending on the value of the boolean object.
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